10.4-10.5 quiz

ratio of areas

a^2/b^2

A= 1/2ans

area of regular polygon is equal to 1/2 * apothem * number of sides * side-length

solving: the similarity ratio of the dimensions of two similar pieces of window glass is 3:5. The smaller piece costs $2.50, what should the larger piece cost?

assume its $2.50 for the area of the smaller (3)^2 / (5)^2 = 9/25 (the ratio of areas) 9/25 = 2.50/x 9x = 62.5 x = $6.94

if two right triangles are similar and the similarity ratio is 4/5, then

the ratio of perimeters is 4/5, and the ratio of areas is 16/25

similarity ratio

the ratio of the lengths of the corresponding sides of two similar polygons a/b

solving: the ratio of lengths of corresponding sides of an octagon is 8/3 and the larger area is 320 ft squared, find the area of the smaller.

(8)^2/(3)^2 = 64/9 (ratio of areas now) 64/9 = 320/x 64x = 320(9) x= 45 ft squared

if given radius of regular polygon to find the area you...

-find central angle and number of sides; use central angle as feta in equation -use A=(n)(1/2)(r^2)(sinFETA)

if given perimeter of regular polygon to find the area you can...

-you can use A=(1/2)ans or (same thing) A=(1/2)aP -divide perimeter by # of sides in polygon -find apothem by using SohCahToa with central angle and half of base (provided by perimeter) -solve by multiplying 1/2 by apothem by the perimeter

radius

A straight line from the center to the circumference of a circle or sphere.

area of a triangle can be

A=(1/2)(a)(b)(sinFETA) OR A=1/2bh

ratio of perimeters

if two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths a/b Ex. In a square, ratio of side lengths=a/b This ratio is then 4a/4b, which equals a/b

in word problems, the price refers to the

ratio of areas (price per square feet sort of thing)

solving: the areas of two similar pentagons is 32 in^2 and 72 in^2. What is their similarity ratio? What is the ratio of their perimeters?

simplify: 32/72 = 4/9 (ratio of areas) similarity ratio and ratio of perimeters are the same: both square root 4/9 which equals 2/3

getting from ratio of area to ratio of perimeter/ similarity ratio

square root ratio of areas

getting from ratio of perimeter/ similarity ratio to ratio of areas

square similarity ratio/ratio of perimeters

a, b, sinFETA

two sides and an included angle